The pentagram map was extensively studied in a series of papers by V. Ovsienko, R. Schwartz and S. Tabachnikov. It was recently interpreted by M. Glick as a sequence
of cluster transformations associated with a special quiver. Using compatible Poisson structures in cluster algebras and Poisson geometry of directed networks
on surfaces, we generalize Glick's construction
to include the pentagram map into a family of geometrically meaningful discrete integrable maps.